# Mathematics

*Major: **Mathematics*

*Degree Awarded: *Master of Science (MS) or Doctor of Philosophy (PhD)

*Calendar Type: Quarter*

*Total Credit Hours:* 45.0 (MS) or 90.0 (PhD)

*Classification of Instructional Programs (CIP) code:* 27.0101

*Standard Occupational Classification (SOC) code:** 15-2021; 15-2041*

## About the Program

The Department of Mathematics is a broadly based academic unit offering instructional programs and carrying on research activities in mathematics. Doctor of Philosophy and Master of Science degrees are offered.

Areas of research specialty among the faculty include applied mathematics, algebraic combinatorics, biomathematics, discrete mathematics, optics, analysis, number theory, numerical analysis, probability and statistics, matrix and operator theory, fluid mechanics, and partial differential equations.

#### Additional Information

For more information about theses graduate programs, visit Department of Mathematics webpage.

## Admission Requirements

Applicants should hold a BS degree in mathematics or the equivalent and meet the University's graduate admission standards. In particular, the student should have had intensive exposure to proof oriented courses, such as real analysis and abstract algebra. Students requesting financial aid are required to take the Graduate Record Examination General Test. Because many of the core courses are two- or three-term sequences beginning in the fall, new students are typically admitted to the programs only in the fall term. Admissions standards for the MS and PhD programs are equivalent.

For additional information on how to apply, visit Drexel University's Graduate Admissions website.

## Master of Science in Mathematics

Students must complete a minimum of 45.0 graduate credits for the MS degree. Of these 15 courses, the following six are required:

Required Courses | ||

MATH 504 | Linear Algebra & Matrix Analysis | 3.0 |

MATH 505 | Principles of Analysis I | 3.0 |

MATH 506 | Principles of Analysis II | 3.0 |

MATH 533 | Abstract Algebra I | 3.0 |

MATH 630 | Complex Variables I | 3.0 |

MATH 633 | Real Variables I | 3.0 |

The remaining 9 courses may be any graduate mathematics courses. In some cases, course substitutions may be made with courses from other departments. Elective courses taken outside the department must receive prior departmental approval in order to be counted toward the degree.

There are no thesis, language, or special examination requirements for the master's degree.

Students seeking a dual MS must satisfy core requirements for both degree programs.

Students should note that some departmental courses, such as Advanced Engineering Mathematics, are foundation courses and do not contribute to the departmental requirements for the degree. They do count toward the University requirements for a degree.

## PhD in Mathematics

Students must complete a minimum of 45 graduate credits for the PhD degree, in addition to the 45.0 required by the MS program for a total of 90.0 credits. Of the 45.0 credits of MS program courses, the following six are required:

Required Courses | ||

MATH 504 | Linear Algebra & Matrix Analysis | 3.0 |

MATH 505 | Principles of Analysis I | 3.0 |

MATH 506 | Principles of Analysis II | 3.0 |

MATH 533 | Abstract Algebra I | 3.0 |

MATH 630 | Complex Variables I | 3.0 |

MATH 633 | Real Variables I | 3.0 |

The remaining 27.0 credits, comprising the MS segment of the PhD program, may be any graduate mathematics courses. In some cases, course substitutions may be made with courses from other departments. Elective courses taken outside the department must receive prior departmental approval in order to be counted toward the degree.

The student must pass a written qualifying exam. The student is allowed two attempts. Students must take exam at the end of their first year, and have a second opportunity in September of their second year.

Students must take a PhD candidacy exam at the end of their second year. Additional coursework to reach the 90.0 credits required for the PhD will be agreed upon with the student's Graduate Advisor. Students should note that some departmental courses, such as MATH 544 Advanced Engineering Mathematics, are foundation courses and do not contribute to the departmental requirements for the degree. They do count toward the University requirements for a degree.

## Facilities

The computing resources of the Mathematics Department include servers dedicated to administrative, research and computation functions. The research server has 4 VCPS's with 8 GB RAM and 40 GB disk space; the computational server pi has the CPU 2.6 GHZ (16 core) AMD Operon with 32 GB RAM and 500 GB disk.

Graduate students and faculty have access to the main Drexel high-performance cluster: Proteus. The university block is available for general purpose computing. Overall, the facility has 2496 computer cores, 9.8 TB RAM (4 GB RAM per core).

In addition to the primary university library, the department itself has a small collection of texts and research books. It is housed in a comfortable room that lends itself to informal research meetings.

## Mathematics Faculty

*(Duke University)*

*Associate Department Head, Mathematics*. Associate Professor. Applied analysis and computing for systems of nonlinear partial differential equations, especially free-surface problems in fluid dynamics.

*(Drexel University)*. Assistant Teaching Professor.

*(University of California at Berkeley)*. Associate Professor. Algebraic combinatorics, representation theory, and complexity theory.

*(University of Pennsylvania)*

*Associate Head of the Mathematics Department*. Professor. Functional analysis, C*-algebras and the theory of group representations.

*(University of Miami)*. Assistant Professor. Homological mirror symmetry, Landau-Ginzburg models, algebraic geometry, symplectic geometry.

*(Drexel University)*. Assistant Teaching Professor. Discrete mathematics and automata theory.

*(Drexel University)*. Assistant Teaching Professor.

*( University of Illinois at Chicago)*. Assistant Teaching Professor. Computational Fluid Dynamics, Free Boundary Problems.

*(Massachusetts Institute of Technology)*. Associate Professor. Intersection of physics, engineering, applied mathematics and computational science.

*(University of California at Berkeley)*. Assistant Teaching Professor. Function theory and operator theory, harmonic analysis, matrix theory.

*(University of Pittsburgh)*. Associate Professor. Biomathematics, dynamical systems, ordinary and partial differential equations and math education.

*(University of Pennsylvania)*. Professor. Geometry; optics; computer vision.

*(Warsaw University)*. Professor. Probability theory and its applications to analysis, combinatorics, wavelets, and the analysis of algorithms.

*(Drexel University)*. Assistant Teaching Professor.

*(The University of North Carolina at Chapel Hill)*. Visiting Assistant Professor. Algebraic Combinatorics and Algebraic Geometry--specifically positivity results for generating polynomials.

*(Kharkov University)*. Associate Professor. Operator theory, systems theory, complex analysis, C*-algebras and harmonic analysis.

*(University of Utah)*. Assistant Teaching Professor. Electromagnetic wave propagation in composite media, optimization and inverse problem.

*(Boston University)*. Associate Professor. Ordinary and partial differential equations, mathematical neuroscience.

*(University of Houston)*. Visiting Assistant Professor. Inverse Problems

*(University of California, San Diego)*

*Undergraduate Advisor*. Professor. Algebraic combinatorics.

*(Rutgers University)*

*Department Head*. Professor. Partial differential equations and numerical analysis, including homogenization theory, numerical methods for problems with rough coefficients, and inverse problems.

*(Drexel University)*. Associate Teaching Professor. Working with Freshmen

*(Omsk State University)*. Associate Teaching Professor. Math education; geometrical modeling.

*(Drexel University)*. Instructor.

*(University of California at Berkeley)*. Associate Professor. Applied mathematics, numerical analysis, symbolic computation, differential geometry, mathematical physics.

*(University of California at Berkeley)*. Associate Professor. Applied mathematics, computed tomography, numerical analysis of function reconstruction, signal processing, combinatorics.

*(Drexel University)*. Associate Teaching Professor.

*(University of Pennsylvania)*. Professor. Probabilistic combinatorics, asymptotic enumeration.

*(Rutgers University)*. Associate Professor. Discrete optimization, combinatorics, operations research, graph theory and its application in molecular biology, social sciences and communication networks, biostatistics.

*(Columbia University)*. Assistant Professor. Partial differential equations, scientific computing and applied mathematics.

*(Courant Institute, New York University)*. Professor. Homotopy theory, operad theory, quantum mechanics, quantum computing.

*(University of Kansas)*. Assistant Professor. Stochastic Calculus, Large Deviation Theory, Theoretical Statistics, Data Network Modeling and Numerical Analysis.

*(Boston University)*. Assistant Teaching Professor.

*(Harvard University)*. Assistant Teaching Professor. Applied statistics, data analysis, calculus, discrete mathematics, biostatistics.

*(Columbia University)*. Instructor.

*(Penn State University)*. Assistant Teaching Professor.

*(Vrije Universiteit, Amsterdam)*. Professor. Matrix and operator theory, systems theory, signal and image processing, and harmonic analysis.

*(Boston University)*

*Graduate Advisor*. Associate Professor. Partial differential equations, specifically nonlinear waves and their interactions.

*(Cornell University)*. Assistant Teaching Professor. Dynamical systems, neurodynamics.

*(Stanford University)*. Professor. Multiscale mathematics, wavelets, applied harmonic analysis, subdivision algorithms, nonlinear analysis, applied differential geometry and data analysis.

## Emeritus Faculty

*(University of Washington)*. Professor Emeritus. Functional analysis, wavelets, abstract harmonic analysis, the theory of group representations.

*(University of Pennsylvania)*. Professor Emeritus. Functional analysis, C*-algebras and group representations, computer science.

*(Temple University)*

*Dean Emeritus*. Professor Emeritus. Mathematics education, curriculum and instruction, minority engineering education.

*(Ohio State University)*. Associate Professor Emeritus. Number theory, approximation theory and special functions, combinatorics, asymptotic analysis.

*(University of Pennsylvania)*. Professor Emeritus. Lie algebras; theory, applications, and computational techniques; operations research.

*(University of California at Davis)*. Professor Emeritus. Probability and statistics, biostatistics, epidemiology, mathematical demography, data analysis, computer-intensive methods.

*(Courant Institute, New York University)*. Professor Emeritus. Applied mathematics, scattering theory, mathematical modeling in biological sciences, solar-collection systems.

*(University of Edinburgh)*. Professor Emeritus. Applied mathematics, special factors, approximation theory, numerical techniques, asymptotic analysis.

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